Bar-On, A., Keller, N.: A 270 attack on the full MISTY1. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 435–456. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4 16
Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling entering the SAT Competition 2020. In: Proceedings of SAT Competition 2020 – Solver and Benchmark Descriptions. Department of Computer Science Report Series b, vol. B-2020-1, pp. 51–53. University of Helsinki (2020)
Biryukov, A., Khovratovich, D., Perrin, L.: Multiset-algebraic cryptanalysis of reduced Kuznyechik, Khazad, and secret SPNs. IACR Trans. Symm. Cryptol. 2016(2), 226–247 (2016)
Boura, C., Canteaut, A.: On the influence of the algebraic degree of F−1 on the algebraic degree of G ◦ F. IEEE Trans. Inf. Theor. 59(1), 691–702 (2013)
Boura, C., Canteaut, A.: Another view of the division property. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 654–682. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4 24
Boura, C., Coggia, D.: Efficient MILP modelings for Sboxes and linear layers of SPN ciphers. IACR Trans. Symmetric Cryptol. 2020(3), 327–361 (2020)
Carlet, C.: Graph indicators of vectorial functions and bounds on the algebraic degree of composite functions. IEEE Trans. Inf. Theor. 66(12), 7702–7716 (2020)
Carlet, C.: Handling vectorial functions by means of their graph indicators. IEEE Trans. Inf. Theor. 66(10), 6324–6339 (2020)
Chen, S., Xiang, Z., Zeng, X., Zhang, S.: On the relationships between different methods for degree evaluation. IACR Trans. Symmetric Cryptol. 2021(1), 411–442 (2021)
Daemen, J., Rijmen, V.: The Design of Rijndael: AES-The Advanced Encryption Standard. Information Security and Cryptography, Springer, Heidelberg (2002). https://doi.org/10.1007/978-3-662-04722-4
Eskandari, Z., Kidmose, A.B., Kölbl, S., Tiessen, T.: Finding integral distinguishers with ease. In: Cid, C., Jacobson, M., Jr., (eds.) Selected Areas in Cryptography – SAC 2018, SAC 2018. LNCS, vol. 11349. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7 6
Gamrath, G., et al.: The SCIP Optimization Suite 7.0. Technical report, Optimization Online (2020)
Fujioka, A., Okamoto, Y., Saito, T.: Security of sequential multiple encryption. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol. 6212, pp. 20–39. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14712-8 2
Göloğlu, F., Rijmen, V., Wang, Q.: On the division property of S-boxes. Cryptology ePrint Archive, Report 2016/188 (2016)
Guo, J., Peyrin, T., Poschmann, A., Robshaw, M.: The LED block cipher. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 326–341. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23951-9 22
Hao, Y., Leander, G., Meier, W., Todo, Y., Wang, Q.: Modeling for three-subset division property without unknown subset. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 466–495. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1 17
Hebborn, P., Lambin, B., Leander, G., Todo, Y.: Lower bounds on the degree of block ciphers. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12491, pp. 537–566. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64837-4 18
Heule, M., Jarvisalo, M., Suda, M., Iser, M., Balyo, T., Froleyks, N.: SAT Competition 2020-Results. https://satcompetition.github.io/2020/index.html
Hu, K., Sun, S., Wang, M., Wang, Q.: An algebraic formulation of the division property: revisiting degree evaluations, cube attacks, and key-independent sums. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12491, pp. 446–476. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64837-4 15
Hu, K., Wang, Q., Wang, M.: Finding bit-based division property for ciphers with complex linear layer. IACR Trans. Symm. Cryptol. 2020(1), 396–424 (2020)
Lambin, B., Derbez, P., Fouque, P.-A.: Linearly equivalent S-boxes and the division property. Des. Codes Crypt. 88(10), 2207–2231 (2020). https://doi.org/10.1007/s10623-020-00773-4
Malviya, A.K., Tiwari, N.: Quantum algorithm to identify division property of a multiset. Arab. J. Sci. Eng. 46(9), 8711–8719 (2021)
Matsui, M.: New block encryption algorithm MISTY. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 54–68. Springer, Heidelberg (1997). https://doi.org/10. 1007/BFb0052334
McCluskey, E.J.: Minimization of Boolean functions. Bell Syst. Tech. J. 35(6), 1417–1444 (1956)
Quine, W.V.: A way to simplify truth functions. Am. Math. Mon. 62(9), 627–631 (1955)
Sasaki, Yu., Todo, Y.: New algorithm for modeling S-box in MILP based differential and division trail search. In: Farshim, P., Simion, E. (eds.) SecITC 2017. LNCS, vol. 10543, pp. 150–165. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69284-5 11
Sinz, C.: Towards an optimal CNF encoding of Boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005). https://doi.org/10.1007/11564751 73
Sun, B., Hai, X., Zhang, W., Cheng, L., Yang, Z.: New observation on division property. Sci. Chin. Inf. Sci. 60(9), 1–3 (2016). https://doi.org/10.1007/s11432-015-0376-x
Sun, L., Wang, W., Wang, M.: Accelerating the search of differential and linear characteristics with the sat method. IACR Trans. Symmetric Cryptol. 2021(1), 269–315 (2021)
Sun, L., Wang, W., Wang, M.Q.: MILP-aided bit-based division property for primitives with non-bit-permutation linear layers. IET Inf. Secur. 14(1), 12–20 (2016)
Todo, Y.: Integral cryptanalysis on full MISTY1. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 413–432. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6 20
Todo, Y.: Structural evaluation by generalized integral property. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 287–314. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5 12
Todo, Y., Morii, M.: Bit-based division property and application to Simon family. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 357–377. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5 18
Todo, Y., Morii, M.: Compact representation for division property. In: Foresti, S., Persiano, G. (eds.) CANS 2016. LNCS, vol. 10052, pp. 19–35. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-48965-0 2
Udovenko, A.: Convexity of division property transitions: theory, algorithms and compact models. Cryptology ePrint Archive, Report 2021/1285 (2021). https://ia. cr/2021/1285
Udovenko, A.: MILP modeling of Boolean functions by minimum number of inequalities. Cryptology ePrint Archive, Report 2021/1099 (2021)
Xiang, Z., Zhang, W., Bao, Z., Lin, D.: Applying MILP method to searching integral distinguishers based on division property for 6 lightweight block ciphers. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 648–678. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6 24
Zhang, W., Rijmen, V.: Division cryptanalysis of block ciphers with a binary diffusion layer. IET Inf. Secur. 13(2), 87–95 (2018)
